Answer:
Step-by-step explanation:
<h3>Solution</h3>
- 6 - 2n - 5< -11
- 1 - 2n < -11
- -2n < -12
- n > 6
<h3>Check</h3>
- n = 10
- 6 - 2*10 - 5 < -11
- 6 - 20 - 5 < -11
- -19 < -11
Graph is the line segment of the right from point 6 not including 6
Answer:
x = 3.5
perimeter of each figure = 54
Step-by-step explanation:
Perimeter of square: 4(3x + 3) 12x + 12
Perimeter of equilateral triangle: 3(5x + 0.5) = 15x + 1.5
Solve for x: 12x + 12 = 15x + 1.5
Grouping like terms results in 10.5 = 3x, which leads to x = 3.5.
Each polygon has a perimeter of 12x + 12, which here is 12(3.5) + 12 = 54
x = 3.5
perimeter of each figure = 54
ANSWER
Quotient:
Remainder:
EXPLANATION
The given functions are
and
We want to find the quotient and the remainder when f(x) is divided by g(x).
We perform the long division as shown in the attachment.
The quotient is
The remainder is
The first step in solving a problem is illustrating it just as what the picture shows. The ladder represents the hypotenuse, or the longest side of the right triangle. It measures 14 feet. The base measures 6 feet. The height of the top of the ladder from the base of the wall is denoted as x. Since this is a right triangle, the special equations for Pythagorean theorems would apply. The equation is
c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the other shorter legs. Substituting the values,
14^2 = 6^2 + x^2
x^2 = 14^2 - 6^2
x^2 = 160
x = 4√10 = 12.65 feet